Download A Bayesian Belief Network

METU Informatics Institute
Min720
Pattern Classification
with Bio-Medical
Applications
Lecture notes 9
Bayesian Belief Networks
Bayesian Belief Networks
• An approach that fits doctor’s need well
• Often used for that reason,
• A graphical-statistical approach that relies on the statistical
relationships among the random variables
• Instead of assuming that the features are statistically
independent, we form relations
• And dependencies among features by way of a graph.
Bayesian Belief Networks
• A Bayesian Belief Network: a knowledge-based graphical
representation that shows a set of variables and their
probabilistic relationships between diseases and symptoms.
• They are based on conditional probabilities, the probability of an
event given the occurrence of another event, such as the
interpretation of diagnostic tests.
•
The Bayesian network can be used to compute the
probabilities of the presence of the possible diseases given
their symptoms.
•
Some of the advantages of Bayesian Network include the
knowledge and conclusions of experts in the form of
Probabilities as an assistance in decision making.
A Simple Bayes Net
P(A), A=1,2
P(B), B=1,2
A
P(D I A,C); D=1,2
D
P(C I A, B), C=0,1
•
•
B
C
Defines ‘causal’ relationships between variables A,B,C,D
C is the child of B and parent of D
Conditional Probability Tables
A,B= 1,1
A,B=1,2
A,B=2,1
A,B=2,2
C=0
0.2
0.2
0.3
0.3
C=1
0.5
0.4
0.05
0.05
Conditional Probability table for C for the example in the previous
page.
Should be available for all nodes
• Usually discrete variables are used; a feature might have a few
discrete values
• Conditional probabilities defined, may be continuous
• Parents and children
• With the application of the Bayes Rule, we can calculate any
configuration of variables
• We need conditional probability tables
• Example: The problem of classifying fish
• Once the nets and joint probability tables are given, we can
calculate any combination of probabilities
• In the fish example, we want to determine the Probability of
salmon and prob. of sea bass if it is wide, dark and caught
in winter in north sea.
• From given probabilities, we deduct the probs of the categories
or any other combination